Abstract: 

The statistical comparison of two multivariate samples is a frequent task, e.g. in biomarker analysis. Parametric and nonparametric multivariate analysis of variance (MANOVA) procedures are well established procedures for the analysis of such data. Which method to use depends on the scales of the endpoints and whether the assumption of a parametric multivariate distribution is meaningful. However, in case of a significant outcome, MANOVA methods can only provide the information that the treatments (conditions) differ in any of endpoints; they cannot locate the guilty endpoint(s). Multiple contrast tests in terms of maximum tests on the contrary provide local test results and thus the information of interest.

The maximum test method controls the error rate by comparing the value of the largest contrast in magnitude to the (1-α)-equicoordinate quantile of the joint distribution of all considered contrasts. The advantage of this approach over existing and commonly used methods that control the multiple type-I error rate, such as Bonferroni, Holm, or Hochberg, is that it is appealingly simple, yet has sufficient power to detect a significant difference in high-dimensional designs, and does not make strong assumptions (such as MTP2) about the joint distribution of test statistics. Furthermore, the computation of simultaneous confidence intervals is possible. The challenge, however, is that the joint distribution of the test statistics used must be known in order to implement the method.

In this talk, we develop a simultaneous maximum Wilcoxon-Mann-Whitney test for the analysis of multivariate data in two independent samples. We hereby consider both the cases of low-and high-dimensional designs. We derive the (asymptotic) joint distribution of the test statistic and propose different bootstrap approximations for small sample sizes. We investigate their quality within extensive simulation studies. It turns out that the methods control the multiple type-I error rate well, even in high-dimensional designs with small sample sizes. A real data set illustrates the application.